This document contains information about different forms of linear equations: slope-intercept form, point-slope form, and a method for finding an equation given two points on a line. It defines each form, provides examples of equations written in the different forms, and includes a set of practice problems with answers for finding equations of lines given characteristics like slope, intercepts, and points on the line.

1. SEC 3-4
JIM SMITH
JCHS
3108.1.2 Determine position using coordinate systems
3108.1.12 Historical development of geometry

2. SLOPE – INTERCEPT FORM
THE EQUATION ON A LINE CAN BE WRITTEN IF WE KNOW
THE SLOPE OF THE LINE AND THE Y-INTERCEPT.
FROM ALGEBRA WE KNOW THIS FORM IS y = mx + b WHERE M
IS THE SLOPE OF THE LINE AND B IS THE Y-INTERCEPT.
IF OUR SLOPE = 4 AND THE Y-INTERCEPT IS 3, THEN y = 4x + 3 .
THE KEY IS HAVING THE “Y” ON ONE SIDE BY ITSELF.
SLOPE Y-INTERCEPT EQUATION
2 8
1 -3
0 6
4 0
y = 2x + 8
y = x – 3
y = 6
y = 4x
EQUATION SLOPE Y-INTERCEPT
Y = 7x – 2
Y = 4x + 5
2Y + 3X = 8
7 -2
4 5
-3 4
2

3. POINT – SLOPE FORM
IF WE’RE GIVEN THE SLOPE OF A LINE AND A POINT ON THAT
LINE OTHER THAN THE Y – INTERCEPT, THEN WE USE THE
POINT – SLOPE FORM
y - y₁ = m ( x - x₁ )
WHERE ( x₁, y₁ ) ARE THE COORDINATES
OF THE POINT ON THE LINE AND m IS THE SLOPE.
SLOPE = 2 LINE PASSES THROUGH ( 3 , 5 )
y – 5 = 2 ( x – 3 ) POINT – SLOPE FORM
y – 5 = 2x – 6
y = 2x - 1 SLOPE – INTERCEPT FORM
YOU CAN FIND THE Y-INTERCEPT BY SOLVING FOR (b)
Y = mx + b
5 = 2(3) + b
5 = 6 + b
B = -1 y = 2x - 1

4. 2 POINTS, NO SLOPE
IF WE HAPPEN TO KNOW 2 POINTS ON A LINE BUT NOT THE SLOPE,
WE NEED TO FIND THE SLOPE FIRST.
A LINE PASSES THROUGH ( 2 , 8 ) AND ( 3 , 10 )
FIND THE SLOPE FIRST
10 – 8
3 – 2
M = 2
USE EITHER ONE OF THE POINTS AND PLUG IN
POINT – SLOPE FORM
Y – 8 = 2 ( x – 2 )
Y – 8 = 2x – 4
Y = 2x + 4
OR
10 – 8 = m ( 3 – 2 )
2 = m
Then use point – slope form

5. 1. Which is an equation of the line in the graph shown?
A. y = 2x – 3 C. y = -2x + 3
B. y = 2x + 3 D. y = -2x - 3
2. Which is an equation of the line with slope 0
and passing through the point at (-2, 3)?
A. y = 3 C. y = 0
B. x = -2 D. y = -2x + 3
3. Which is an equation of the line with slope = 3, and y-intercept = -1 .
A. y = -x + 3 C. y = 3x - 1
B. y = x - 3 D. y = -3x + 1
4. Write the equation of the line perpendicular to y = ½ x + 6
that passes through the point (3,-13)
A. y = 1/2x - 6 C. y = 2x + 6
B. y = -2x - 7 D. y = -2x + 7
5. Write the equation of the line that has an x-intercept of –6
and a y-intercept of 3.
A. y = 3x + 5 C. y = 1/2x - 3
B. y = -2x + 3 D. y = 1/2x + 3
From glencoe.com
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